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Properties of Rational Functions
Section 5.4 Properties of Rational Functions
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OBJECTIVE 1
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{ x | x ≠ -2 , x ≠ -6 } { x | x ≠ -4 } All Reals All Reals { x | x ≠ -2 }
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OBJECTIVE 2
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x = - 3 x = 2 and x = - 2 x = - 1 and x = - 4 x = 2
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OBJECTIVE 3
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A rational function R(x) is proper if the degree of the
numerator is less than the degree of the denominator.
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y = 0 is the horizontal asymptote
Degree of numerator < degree of denominator y = 0 is the horizontal asymptote
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2 Degree of numerator = degree of denominator , y = 2x2 /x2 = 2 y = 2
___________________ Degree of numerator = degree of denominator , y = 2x2 /x2 = 2
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Degree of numerator = degree of denominator , y = 5x6 /2x6 = 5/2
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x + 6 Oblique Asymptote is y = x + 6 ____________ __________ 13
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